Composite Gridshell Prototypes

The goal of the design process is to identify a gridshell structure that works and which respect as faithfully as possible the architectural project – a shape and a program. It represents “the path from shape to structure”. Its progress, sequential and iterative, revolves around three major stages: shape, mesh and structure (Fig. 7). It is not trivial to go through this complex process. Indeed, for each step, the method, the tool, the criteria, that offer both a sufficient explorative richness to find out enough candidate solution, and the means to evaluate and compare the suitability of those solution, have to be found.

The first step of the process consists in building a precise geometric model from the sketch of the architect and to evaluate its mechanical potential (Fig. 8). At this stage, the goal is to estimate the probability a given shape would lead to the generation of a structurally feasible gridshell. The figure shows a selection of 3 slightly different 3D shapes, derived from the targeted shape, based on an analysis of their principal curvatures. Stresses in the grid are mainly due to the bending of the profiles. They derive directly from their geometric curvature. Thus, the principal curvatures of the surface – because they give a qualitative measurement of the local curvature of any curve drawn on a surface – are relevant indicators to evaluate the stress rate of a grid laying on it. Particularly, one should ensure the following condition is satisfied everywhere, where r is the pipe’s outer radius, Rmin is the minimum principal radius, E is the flexural modulus, σk,flex the characteristic flexural strength (§5.3) and γlt the long-term partial coefficient of material resistance. Ideally, the shape is controlled by few key parameters. Thus, it can be adapted and optimized through an iterative process, towards this criterion (1).

During the second step, the candidate surface is meshed and the mechanical potential of the resulting grid is evaluated. At this stage, we try to estimate the probability a given mesh could lead to the generation of a viable gridshell structure (Fig. 9). Simultaneously, meshes are compared according to their architectural relevance. This time, the geometric curvature of the polylines drawn on the surface is the criterion to characterize the mechanical potential of the grid. In particular, one should ensure the following condition is satisfied everywhere, where Rspline is the spline’s local curvature radius: The mesh is obtained by the compass method, described in [11], which develops a regularly spaced grid on a surface from two secant directrix. For a given shape there are an infinite number of meshes. The aim is to identify at least one grid, suitable towards architectural and structural criteria (Fig. 9). The figure shows resulting meshes and flat grids, depending the directrix. The laboratory tried various numerical methods to generate such grids [12]. Here, a specific software [13], developed for rhino & grasshopper, allows generating this kind of mesh on any nurbs surface. It performs the following elementary operations: surface meshing with the compass method, trimming, control of geometry’s integrity and flattening of the grid. The tool also generates automatically a text file, which can be imported in structural analysis software, containing all the required information to perform the formfinding of the structure. An add-on facilitates loads application of various complexities (snow, wind, etc.), which is tricky for free forms.

In this project, one can identify 4 major structural details : the swivel coupler for connecting com- posite tubes to assemble the grid (Figure 8a); the steel sleeve for connecting several composite tubes to make long members from initially short piece of tubes (Figure 8b); ground anchorages for fixing the structure to the concrete slab (Figure 8c) and the lacing edge beam of the fabric (Figure 8d). Note that the tricky issue of connecting steel and composite parts is solved in a similar way through sleeve and anchorage details.

Sleeves are major components in the structural system. The presented component is a great innovation compared to the composite gridshells built previously, where members were simply interrupted or overlapped. By establishing mechanical and architectural continuities between pipes, this sleeve brings closer the real behavior and the theoretical behavior of the shell.

The sleeve is a steel system that sets up mechanical continuity between two adjacent composite pipes for both tension and bending. It is made of three parts: two connectors linked by a threaded rod (Fig. 12b). Each connector is a 48.3×2.9mm steel pipe, slightly larger than the composite pipes on which it is put on, with a welded M20 nut at one of his end. The connector is pinned to the composite pipe with three 10mm bolts. Some structural adhesive is also employed to fill gaps and to guaranty a good rigidity of the assembly. However, the sleeve is designed ignoring the adhesive contribution to the mechanical strength of the system. A M20 threaded rod links the two connectors. It allows tension forces and bending moments to pass form one pipe to the other. It cannot transfer any twisting moment.

Tension forces are transferred from the composite pipe to the connector through shear in the pins. Thanks to a lower bearing resistance in the composite than in the steel, each of the three pins can be gradually loaded. When loading the system, at first, only one of the three pins is really in contact with both the steel pipe and the composite pipe, because of inevitable small manufacturing gaps. When increasing the axial load, this pin starts to “eat” into the composite pipe until the second pin comes also in contact (Fig. 13). This scheme is reproduced until another failure mode happened. For this mode of composite failure, which prevails in this case, the total bearing capacity of the assembly is thus three times the capacity of a single pin.

Bending moments are transferred through the threaded rod of the sleeve. This part is designed to reach simultaneously the two following qualitative criterions. Firstly, the rod bending stiffness should be roughly equivalent to the composite bending stiffness itself to preserve curvature’s continuity along the system. Note that this continuity is of prime importance from an architectural point of view. Secondly, the steel quality of the rod should be adjusted so it starts its plastification when the composite pipe tends to approach its maximum design stress (a third of the yield stress). Thus, the rod acts as a “fuse” which concentrates rotational deformations avoiding failures in the critical elements of the structure (the composite pipes).

Beyond the technical difficulties related to both design and structural analysis of the shell, the regula- tory framework was a vital issue for the project’s success. Because it was the first time a structure of this kind would host regularly a large number of people in a long-term period, the question of its re- liability over time was a major issue. To be built the gridshell had to comply with existing standards, which do not take into account such an innovative edifice, all in composite material. The strategy adopted to bypass this obstacle consisted in making the most of the existing regulatory framework to justify the compliance of a structure that would not, at first sight, be taken into account by stan- dards that does not include composite materials. As far as possible, the design was led in compliance with the Eurocodes, where the structural design is made according to limit states under normalized loadings (self-weight, snow, wind, etc.). Despite the Eurocodes do not directly take into account com- posite materials, they propose some probabilistic methods to introduce new materials (Annexe D). As far as possible, the mechanical properties of the GFRP pipe were determined by tests in conformance with these methods. Otherwise, values where taken according to the Eurocomp [16]. In some cases, as the sleeve, the design of the construction details has also benefited from this approach.